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In this paper we provide a convergence analysis of some variational methodsalternative to the classical Tikhonov regularization, namely Ivanovregularization (also called method of quasi solutions) with some versions ofthe discrepancy principle for choosing the regularization parameter, andMorozov regularization (also called method of the residuals). After motivatingnonequivalence with Tikhonov regularization by means of an example, we provewell-definedness of the Ivanov and the Morozov method, convergence in the senseof regularization, as well as convergence rates under variational sourceconditions. Finally, we apply these results to some linear and nonlinearparameter identification problems in elliptic boundary value problems.

inverse problems

On convergence and convergence rates for Ivanov and Morozov  regularization and application to some parameter identification problems in  elliptic PDEs